Optimization of the adhesive joint Iosipescu specimen for pure shear test

This paper reviews some of the difficulties encountered in achieving a uniform stress distribution within the adhesive layer of bonded Iosipescu shear test specimens. The asymptotic singular stress field at the terminus of a skewed bimaterial interface, intersecting the straight free surface of the wedge, has been studied macroscopically and microscopically using the finite element method (FEM) and the finite element iterative method (FEIM). Different mechanical properties of the adhesives and adherends, and various skewed interface angles have been considered in this study. A critical skewed interface angle, _c=126°, has been found beyond which the interfacial stress singularity vanishes. This critical angle is independent of the elastic properties of the adhesives and adherends. Based on the results obtained in the present investigation, in conjunction with recently reported research on sharp notches [7, 21–23], an optimized adhesive joint Iosipescu specimen geometry is proposed. This specimen should be capable of generating a uniform shear stress state within its adhesive layer under pure shear loading conditions.     

Strain and crack distribution in concrete during drying

Uneven shrinkage behavior between cement paste and rock aggregate takes place when concrete is subjected to drying. Possible consequences including internal damage and strain distribution need to be researched to understand the changes in concrete properties over time. In this study, strain distributions over the cross section of sliced concrete specimens with age were determined using a digital image correlation method (DICM). After shrinkage had developed, crack distributions were visually observed using a fluorescent epoxy impregnation method (FEIM). High correlation was found between expansive strain at the maximum principal strain distribution obtained with DICM and positions of cracks obtained with FEIM, suggesting that DICM can be applied to the damage evaluation of a concrete cross section over time. Even the present DICM and FEIM studies are results of surface cracking of specimens, which is strongly affected by the water transfer process and resultant three dimensional stress distribution, the following findings were obtained: the area of internal fine cracks increased with increase in aggregate size, correlation was confirmed between the area of fine cracks and macroscopic strain of concrete, and two types of fine cracks were confirmed—cracks restrained by aggregate and interfacial cracks between aggregate and mortar as a result of stress arch formation.     

A nine node finite element for analysis of geometrically non-linear shells

A nine node finite element is presented for the analysis of thin shell structures undergoing large deflection. The finite element formulation is based on the concept of degenerate solid shell element and the Hellinger-Reissner principle with independent strain. Three versions of assumed independent strain are selected to suppress spurious kinematic modes. One version leads to a finite element model which is kinematically stable at element level while the other two give globally stable models. Numerical tests indicate that the finite element model which is stable at element level may reveal the locking effect in certain cases. However, the other two models are free of locking.     

New basis functions and computational procedures for p-version finite element analysis

New basis functions and solution procedures for p-version finite element analysis are described. They are used in a highly efficient p-version finite element solver for linear elastostatics and dynamics, which has been used in an industrial environment for over two years. Using two sample applications it is shown that, using the techniques proposed here, p-version finite element analysis can have a substantially lower computational cost, for given accuracy, than standard finite element methods. This makes the industrial applicability of p-version finite element analysis much wider than is commonly believed.     

Numerical Methods for Constrained Elliptic Optimal Control Problems with Rapidly Oscillating Coefficients

In this paper we use two numerical methods to solve constrained optimal control problems governed by elliptic equations with rapidly oscillating coefficients: one is finite element method and the other is multiscale finite element method. We derive the convergence analysis for those two methods. Analytical results show that finite element method can not work when the parameter $\varepsilon$ is small enough, while multiscale finite element method is useful for any parameter $\varepsilon$.     

A comparative study of the boundary and finite element methods for the Helmholtz equation in two dimensions

The performance of the boundary and finite element methods for the Helmholtz equation in two dimensions is investigated. To facilitate the comparison, the system of linear equations arising from the finite element formulation is reduced to a smaller system involving the boundary values of the unknown function and its normal derivative alone. The difference between the boundary and finite element solutions is then expressed in terms of a difference matrix operating on the boundary data. Numerical investigations show that the boundary element method is generally more accurate than the finite element method when the size of the finite elements is comparable to that of the boundary elements, especially for the Dirichlet problem where the boundary values of the solution are specified. Exceptions occur in the neighborhood of isolated points of the Helmholtz constant where eigenfunctions of the boundary integral equation arise and the boundary element method fails to produce a unique solution.     

Multiphase hybrid stress finite element analysis of heterogeneous media by simple mesh: One element with one interface

In this paper, a finite element method is proposed to analyze the microscopic and macroscopic mechanical behaviors of heterogeneous media with randomly distributed inclusions. A simple mesh partitioned the domain into regular quadrilateral or triangular elements, where one element may contain two phases. An assumed stress hybrid formulation is implemented in the finite element model and the functional is derived for an element containing two phases. Numerical examples were used to study the microscopic and macroscopic properties of the composites, such as the effective modulus, to validate of the proposed model. The results show that the proposed multiphase hybrid stress finite element model can accurately measure the stress fields of materials with arbitrary microstructural distributions and improve computational efficiency by about 30 to 1500 times in comparison with the traditional displacement based finite element method.     

ASYMPTOTIC SOLUTIONS FOR PREDICTED NATURAL FREQUENCIES OF TWO-DIMENSIONAL ELASTIC SOLID VIBRATION PROBLEMS IN FINITE ELEMENT ANALYSIS

In order to assess the discretization error of a finite element solution, asymptotic solutions for predicted natural frequencies of two-dimensional elastic solid vibration problems in the finite element analysis are presented in this paper. Since the asymptotic solution is more accurate than the original finite element solution, it can be viewed as an alternative solution against which the original finite element solution can be compared. Consequently, the discretization error of the finite element solution can be evaluated. Due to the existence of two kinds of two-dimensional problems in engineering practice, both the plane stress problem and the plane strain problem have been considered and the corresponding asymptotic formulae for predicted natural frequencies of two-dimensional solids by the finite element method have been derived from the fact that a discretized finite element system approaches a continuous one if the finite element size approaches zero. It has been demonstrated, from the related numerical results of three examples, that the present asymptotic solution, which can be obtained by simply using the corresponding formula without any further finite element calculation, is indeed more accurate than the original finite element solution so that it can be considered as a kind of corrected solution for the discretization error estimation of a finite element solution.     

粗网格划分下的箱梁三维实体有限元分析方法

针对现有箱梁分析方法普遍存在的计算精度与计算效率之间矛盾的问题,提出了粗网格划分下的箱梁三维实体有限元分析方法。在充分考虑箱梁受力变形特点的基础上,以修正的Hellinger-Reissner变分原理为基础,通过合理引入非协调位移插值项,构造出直角坐标系下的六面体八结点杂交应力单元8N21β和柱坐标系下的六面体八结点杂交应力单元8N21βc,分别用于粗网格划分下的直箱梁和曲线箱梁的三维实体有限元分析。数值算例表明:8N21β单元和8N21βc单元在粗网格划分下具有较高的计算精度,能有效提高箱梁三维实体有限元分析的计算效率。     

Anomalous behavior of bilinear quadrilateral finite elements for modeling cohesive cracks with XFEM/GFEM

The performance of partition‐of‐unity based methods such as the generalized finite element method or the extended finite element method is studied for the simulation of cohesive cracking. The focus of investigation is on the performance of bilinear quadrilateral finite elements using these methods. In particular, the approximation of the displacement jump field, representing cohesive cracks, by extended finite element method/generalized finite element method and its effect on the overall behavior at element and structural level is investigated. A single element test is performed with two different integration schemes, namely the Newton‐Cotes/Lobatto and the Gauss integration schemes, for the cracked interface contribution. It was found that cohesive crack segments subjected to a nonuniform opening in unstructured meshes (or an inclined crack in a structured finite element mesh) result in an unrealistic crack opening. The reasons for such behavior and its effect on the response at element level are discussed. Furthermore, a mesh refinement study is performed to analyze the overall response of a cohesively cracked body in a finite element analysis. Copyright © 2013 John Wiley & Sons, Ltd.     

On fracture analysis using an element overlay technique

In this paper, an element overlay technique (s-FEM [Comput. Struct. 43 (1992) 539]) is applied to various two dimensional linear fracture problems. When s-FEM is adopted, local finite element model concerning cracks can be built independently from the global finite element mesh for modeling overall structure. The local model is superposed on the global one. Therefore, it is tractable to introduce cracks in an existing finite element model. The accuracy of s-FEM is critically examined and it is found that the size of local mesh region needs to be larger than or roughly equal to that of an element in the global mesh.     

A solid‐like shell element allowing for arbitrary delaminations

In this contribution a new finite element is presented for the simulation of delamination growth in thin‐layered composite structures. The element is based on a solid‐like shell element: a volume element that can be used for very thin applications due to a higher‐order displacement field in the thickness direction. The delamination crack can occur at arbitrary locations and is incorporated in the element as a jump in the displacement field by using the partition of unity property of finite element shape functions. The kinematics of the element as well as the finite element formulation are described. The performance of the element is demonstrated by means of two examples. Copyright © 2003 John Wiley & Sons, Ltd.     

On the dynamic behaviour of the Timoshenko beam finite elements

First, various finite element models of the Timoshenko beam theory for static analysis are reviewed, and a novel derivation of the 4 × 4 stiffness matrix (for the pure bending case) of the superconvergent finite element model for static problems is presented using two alternative approaches: (1) assumed-strain finite element model of the conventional Timoshenko beam theory, and (2) assumed-displacement finite element model of a modified Timoshenko beam theory. Next, dynamic versions of various finite element models are discussed. Numerical results for natural frequencies of simply supported beams are presented to evaluate various Timoshenko beam finite elements. It is found that the reduced integration element predicts the natural frequencies accurately, provided a sufficient number of elements is used. The research reported herein is supported by theOscar S. Wyatt Endowed Chair.     

长输管道悬索跨越结构静动力性能的有限元分析

应用ANSYS有限元程序,建立长输管道悬索跨越工程原型和1∶8试验模型的有限元计算模型,对有限元计算模型进行静力、模态和地震反应的有限元分析。结果表明:静力计算和模态分析中,计算结果与试验结果吻合很好,2个有限元模型的计算结果能较好地满足模型设计相似比,试验模型能较好地反映原型结构的性态;地震反应分析和试验中,输入的最大横向和竖向地震反应加速度折合原型均超过0.4g,但模型构件未发生破损,结构体系保持稳定,表明悬索跨越结构具有抗御地震烈度9度而保持使用功能的能力,但有限元模型地震反应计算结果与试验实测值之间存在着一定差异,分析了造成差异的原因。     

考虑接头作用的全复合材料桁架结构多尺度分析

为提高全复合材料桁架分析的精度和效率,引入结构多尺度有限元思想,对接头进行精细化建模,通过建立两点位移约束实现不同尺度模型连接,从而将接头模型嵌入宏观桁架模型,并针对具体制备工艺赋予桁架材料属性。为验证多尺度模型的优势,同时进行全复合材料桁架实验,以及分别基于全部梁单元模型和全部实体单元模型的有限元分析。对比相关模型的计算精度与效率,结果表明多尺度模型能够较好地兼顾计算精度与效率。该文针对全复合材料桁架的结构多尺度有限元建模方法,可精确分析全复合材料桁架承载性能,并且能够提供有效的局部信息,可用于分析其他包含复杂细节构造的大尺度复合材料结构。     

膜结构有限元分析中的平面单元与曲面单元的比较

在对膜结构进行有限元模拟时,通常采用两种面单元形式——平面常应变三角形单元和六结点曲面三角形等参元,究竟哪一种单元形式更优一直是存在争议的问题。首先就这两种单元的有限元格式进行探讨,比较了它们在位移模式、几何方程及刚度矩阵等方面的力学本质差异;然后,通过一些典型算例,比较了它们在计算精度和计算效率等方面的优劣。分析结果表明:在有限元格式方面,曲面三角形等参元较之平面常应变三角形单元更为完备,更加符合结构的实际受力特征;在计算精度和计算效率方面,曲面三角形等参元也要优于平面常应变三角形单元;因此,从结构精细化分析的角度来看,宜采用曲面三角形等参元来进行膜结构有限元分析。     

Simulation of two dimensional unilateral contact using a coupled FE/EFG method

In this paper, simulation of two dimensional unilateral contact problems using a coupled finite element/element free Galerkin method is proposed. For the analysis, the element free Galerkin method and Galerkin formulation for two dimensional elasticity problems are considered. Then, the penalty method for imposition of contact constraint is proposed. The finite element shape functions are used in the penalty term of contact constraint. Finally, the accuracy of the presented method is verified through some examples. The numerical results have demonstrated that the presented approach is simple and accurate for frictionless contact analysis of 2D solids.     

A simple finite element model for vibration analyses induced by moving vehicles

This study developed a simple finite element method combining the moving wheel element, spring–damper element, lumped mass and rigid link effect to simulate complicated vehicles. The advantages of this vehicle model are (1) the dynamic matrix equation is symmetric, (2) the theory and formulations are very simple and can be added to a standard dynamic finite element codes easily and (3) very complicated vehicle models can be assembled using the proposed elements as simple as the traditional finite element method. The Fryba's solution of a simply supported beam subjected to a moving two‐axle system was analysed to validate this finite element model. For a number of numerical simulations, the two solutions are almost identical, which means that the proposed finite element model of moving vehicles is considerably accurate. Field measurements were also used to validate this vehicle model through a very complicated finite element analysis, which indicates that the current moving vehicle model can be used to simulate complex problem with acceptable accuracy. Copyright © 2006 John Wiley & Sons, Ltd.     

Singular stress analysis of an anisotropic elastic medium containing polygonal holes using a novel hybrid finite element method

A novel hybrid finite element method based on a numerical procedure is proposed to compute singular field near V-shaped notch corners in an anisotropic material containing polygonal holes. The finite element method is established by the following three steps: (1) an ad hoc one-dimensional finite element formulation is employed to determined numerical eigensolutions of the singular field near an V-shaped notch corner; (2) a super corner tip element is constructed to determine the strength of the singular field, in which the independent assumed stress fields are extracted from the eigensolutions; (3) a novel hybrid finite element equation is obtained by coupling the super corner tip element with the conventional hybrid stress elements. In numerical examples, generalized stress intensity factors for interactions between two polygonal holes with various geometry, space position and material property are mainly discussed. All the numerical results show that present method yields satisfactory singular stress field solutions with fewer elements. Compared with the conventional finite element methods and integral equation methods, the present method is more suitable for dealing with micromechanics of anisotropic materials.     

Propagation of transient SH-waves in a dipping structure by finite- and boundary element methods

Summary The boundary and the finite element formulations for the equations of elasticity are presented and applied to the problem of propagation of transient SH-waves in dipping layers overlying a half-space. When the finite element formulation is used, appropriate boundary conditions are imposed on the additional boundary dividing the half-space into a finite and an infinite region. These conditions ensure the transmission of waves across this boundary. When the boundary element method is applied, it is necessary to satisfy the radiation conditions. Theoretical seismograms for the displacement on the surface of the half-space are presented. They show that, for a specific case, the agreement between the two methods is satisfactory. The results can be compared with those found by the exact method of generalized rays in order to check the validity of the finite and the boundary element methods for the specific problem studied in this paper.